Repr\'esentations cohomologiques isol\'ees, applications cohomologiques

We give a new proof of a Theorem of Vogan which classify the cohomological representations of a real semisimple Lie group $G$ which are isolated in the unitary dual of $G$. We investigate the same question in the automorphic dual, and obtain partial results. We derive applications of all this results (or conjectures) to the study of the cohomology of arithmetic locally symmetric spaces.